Schreyer resolution of modules over formal power series
Commutative Algebra
2026-07-07 v1
Abstract
Standard bases of modules over algebras of formal power series play the same role as Gr\"obner bases of modules over polynomial algebras. In this article, we first prove the analogue of the diamond lemma for modules over formal power series; it characterises standard bases in terms of unique remainders and standard representations. Then, using standard representations, we provide a method to construct a standard basis of the module of syzygies of a standard basis. This construction can be applied inductively to obtain a free resolution, similar to the Schreyer resolution, for finitely presented modules over formal power series.
Cite
@article{arxiv.2607.06635,
title = {Schreyer resolution of modules over formal power series},
author = {Cyrille Chenavier and Thomas Cluzeau and Adya Musson-Leymarie},
journal= {arXiv preprint arXiv:2607.06635},
year = {2026}
}